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Chapter 16: Problem 53

A \(0.100 \mathrm{M}\) solution of cyanic acid (HCNO) is \(5.9 \%\) ionized. Using this information, calculate [CNO^ \(\left.^{-}\right],\left[\mathrm{H}^{+}\right],[\mathrm{HCNO}],\) and \(K_{a}\) for cyanic acid.

Short Answer

Expert verified
In a 0.100 M solution of cyanic acid (HCNO) that is 5.9% ionized, the concentrations of CNO⁻ and H⁺ are both 0.0059 M, while the concentration of non-ionized HCNO is 0.0941 M. The ionization constant, Ka, for cyanic acid is approximately \(3.70 \times 10^{-4}\).

Step by step solution

01

Calculate the ionized concentration of HCNO

First, we need to calculate the ionized concentration of HCNO. To do this, we simply multiply the initial concentration by the percentage ionized (as a decimal). Ionized concentration of HCNO = (Initial concentration) × (Percentage ionized) Ionized concentration of HCNO = (0.100 M) × (5.9/100) \[ Ionized \ concentration \ of \ HCNO = 0.0059 \ M \]
02

Determine the concentrations of CNO⁻ and H⁺

Since HCNO is a weak monoprotic acid, we can assume that every ionized HCNO molecule produced one H⁺ ion and one CNO⁻ ion. Therefore, the concentrations of CNO⁻ and H⁺ are equal to the ionized concentration of HCNO. \[ [CNO^-] = [H^+] = 0.0059 \ M \]
03

Calculate the concentration of non-ionized HCNO

To find the concentration of non-ionized HCNO, we can subtract the ionized concentration from the initial concentration: Non-ionized HCNO concentration = (Initial concentration) - (Ionized concentration) \[ [HCNO] = 0.100 \ M - 0.0059 \ M = 0.0941 \ M \]
04

Calculate the ionization constant (Ka)

Now that we have the concentrations of HCNO, CNO⁻, and H⁺, we can find Ka using the ionization equilibrium formula: \[ K_{a} = \frac{[CNO^-][H^+]}{[HCNO]} \] Plugging in the concentrations, we get: \[ K_{a} = \frac{(0.0059 \ M)(0.0059 \ M)}{0.0941 \ M} \] Calculating the Ka value: \[ K_{a} ≈ 3.70 \times 10^{-4} \] In conclusion, the concentrations of CNO⁻, H⁺, and HCNO are 0.0059 M, 0.0059 M, and 0.0941 M, respectively. The ionization constant, Ka, for cyanic acid is approximately 3.70 x 10⁻⁴.

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